Dirac dispersion in two-dimensional photonic crystals

Advances in OptoElectronics

Volumn 2012, Issue , 2012, Pages

  Chan, C T ^a   Hang, Zhi Hong ^a   Huang, Xueqin ^a  

^a HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

BAND DISPERSIONS; BERRY PHASE; DEGENERATE STATE; DISPERSION SURFACE; EFFECTIVE MEDIUM; EIGEN MODES; FLAT BAND; MONOPOLE AND DIPOLE; MULTIPLE-SCATTERING THEORY; TWO-DIMENSIONAL PHOTONIC CRYSTALS; ZONE BOUNDARIES;

FRUITS; METAMATERIALS; REFRACTIVE INDEX;

DISPERSION (WAVES);

EID: 84869046653     PISSN: 1687563X     EISSN: 16875648     Source Type: Journal    
DOI: 10.1155/2012/313984     Document Type: Review

References (82)

1. Dirac P. A. M., The quantum theory of the electron. Proceedings of the Royal Society A 1928 117 610
2. Novoselov K. S., Geim A. K., Morozov S. V., Jiang D., Zhang Y., Dubonos S. V., Grigorieva I. V., Firsov A. A., Electric field in atomically thin carbon films. Science 2004 306 5696 666 669 2-s2.0-7444220645 10.1126/science.1102896 (Pubitemid 39440910)
3. Novoselov K. S., Geim A. K., Morozov S. V., Jiang D., Katsnelson M. I., Grigorieva I. V., Dubonos S. V., Firsov A. A., Two-dimensional gas of massless Dirac fermions in graphene. Nature 2005 438 7065 197 200 2-s2.0-27744534165 10.1038/nature04233 (Pubitemid 41599867)
4. Zhang Y., Tan Y. W., Stormer H. L., Kim P., Experimental observation of the quantum Hall effect and Berry's phase in graphene. Nature 2005 438 7065 201 204 2-s2.0-27744475163 10.1038/nature04235 (Pubitemid 41599868)
5. Gusynin V. P., Sharapov S. G., Unconventional integer quantum hall effect in graphene. Physical Review Letters 2005 95 14 146801
6. Novoselov K. S., Jiang Z., Zhang Y., Morozov S. V., Stormer H. L., Zeitler U., Maan J. C., Boebinger G. S., Kim P., Geim A. K., Room-temperature quantum hall effect in graphene. Science 2007 315 5817 1379 2-s2.0-33947176113 10.1126/science.1137201 (Pubitemid 46399539)
7. Katsnelsona M. I., Zitterbewegung, chirality, and minimal conductivity in graphene. The European Physical Journal B 2006 51 2 157 160 10.1140/epjb/e2006-00203-1 (Pubitemid 43876887)
8. Cserti J., David G., Unified description of Zitterbewegung for spintronic, graphene, and superconducting systems. Physical Review B 2006 74 17 172305 10.1103/PhysRevB.74.172305 (Pubitemid 44771668)
9. Rusin T. M., Zawadzki W., Transient Zitterbewegung of charge carriers in mono and bilayer graphene, and carbon nanotubes. Physical Review B 2007 76 195439
10. David G., Cserti J., General theory of the Zitterbewegung. Physical Review B 2010 81 121417
11. Castro Neto A. H., Guinea F., Peres N. M. R., Novoselov K. S., Geim A. K., The electronic properties of graphene. Reviews of Modern Physics 2009 81 1 109 162 2-s2.0-59949098337 10.1103/RevModPhys.81.109
12. Katsnelson M. I., Novoselov K. S., Geim A. K., Chiral tunnelling and the Klein paradox in graphene. Nature Physics 2006 2 9 620 625 2-s2.0-33748296088 10.1038/nphys384 (Pubitemid 44328348)
13. Morozov S. V., Novoselov K. S., Katsnelson M. I., Schedin F., Ponomarenko L. A., Jiang D., Geim A. K., Strong suppression of weak localization in graphene. Physical Review Letters 2006 97 1 2-s2.0-33745749916 10.1103/PhysRevLett.97.016801 016801 (Pubitemid 44015290)
14. Geim A. K., MacDonald A. H., Graphene: exploring carbon flatland. Physics Today 2007 60 8 35 41 2-s2.0-36348944051 10.1063/1.2774096
15. Geim A. K., Novoselov K. S., The rise of graphene. Nature Materials 2007 6 3 183 191 2-s2.0-33847690144 10.1038/nmat1849 (Pubitemid 46353764)
16. Plihal M., Maradudin A. A., Photonic band structure of two-dimensional systems: the triangular lattice. Physical Review B 1991 44 16 8565 8571 2-s2.0-4243877927 10.1103/PhysRevB.44.8565
17. Sepkhanov R. A., Bazaliy Y. B., Beenakker C. W. J., Extremal transmission at the Dirac point of a photonic band structure. Physical Review A 2007 75 6 2-s2.0-34347336443 10.1103/PhysRevA.75.063813 063813 (Pubitemid 47014667)
18. Diema M., Koschny T., Soukoulis C. M., Transmission in the vicinity of the Dirac point in hexagonal photonic crystals. Physica B 2010 405 14 2990 2995 2-s2.0-77954314661 10.1016/j.physb.2010.01.020
19. Sepkhanov R. A., Nilsson J., Beenakker C. W. J., How to detect the pseudospin-1/2 Berry phase in a photonic crystal with a Dirac spectrum. Physical Review B 2008 78 045122
20. Zhang X., Observing Zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal. Physical Review Letters 2008 100 11 113903 10.1103/PhysRevLett.100.113903 (Pubitemid 351457202)
21. Raghu S., Haldane F. D. M., Analogs of quantum Hall effect edge states in photonic crystals. Physical Review A 2008 78 033834
22. Haldane F. D. M., Raghu S., Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Physical Review Letters 2008 100 013904
23. Ochiai T., Onoda M., Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states. Physical Review B 2009 80 15 155103 10.1103/PhysRevB.80.155103
24. Ochiai T., Topological properties of bulk and edge states in honeycomb lattice photonic crystals: the case of TE polarization. Journal of Physics 2010 22 22 225502 10.1088/0953-8984/22/22/225502
25. Yablonovitch E., Inhibited spontaneous emission in solid-state physics and electronics. Physical Review Letters 1987 58 20 2059 2062 10.1103/PhysRevLett.58.2059
26. John S., Strong localization of photons in certain disordered dielectric superlattices. Physical Review Letters 1987 58 23 2486 2489 10.1103/PhysRevLett. 58.2486
27. Ho K. M., Chan C. T., Soukoulis C. M., Existence of a photonic gap in periodic dielectric structures. Physical Review Letters 1990 65 25 3152 3155 10.1103/PhysRevLett.65.3152
28. Wang Z., Chong Y. D., Joannopoulos J. D., Soljacic M., Reflection-free one-way edge modes in a gyromagnetic photoniccrystal. Physical Review Letters 2008 100 1 013905 10.1103/PhysRevLett.100.013905 (Pubitemid 351388411)
29. Yu Z., s Veronis G., Wang Z., Fan S., One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal. Physical Review Letters 2008 100 2 023902 10.1103/PhysRevLett.100.023902
30. Wang Z., Chong Y., Joannopoulos J. D., Soljaić M., Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 2009 461 7265 772 775 2-s2.0-70349928588 10.1038/nature08293
31. Ao X., Lin Z., Chan C. T., One-way edge mode in a magneto-optical honeycomb photonic crystal. Physical Review B 2009 80 3 033105 10.1103/PhysRevB.80.033105
32. Poo Y., Wu R. X., Lin Z., Yang Y., Chan C. T., Experimental realization of self-guiding unidirectional electromagnetic edge states. Physical Review Letters 2011 106 9 093903 10.1103/PhysRevLett.106.093903
33. Zhang X., Liu Z., Extremal transmission and beating effect of acoustic waves in two-dimensional sonic crystals. Physical Review Letters 2008 101 26 264303 10.1103/PhysRevLett.101.264303
34. Veselago V. G., The electrodynamics of substances with simultaneously negative values of ε and μ Soviet Physics Uspekhi 1968 10 4 509 10.1070/PU1968v010n04ABEH003699
35. Shelby R. A., Smith D. R., Schultz S., Experimental verification of a negative index of refraction. Science 2001 292 5514 77 79 2-s2.0-0035815370 10.1126/science.1058847 (Pubitemid 32289127)
36. Smith D. R., Padilla W. J., Vier D. C., Nemat-Nasser S. C., Schultz S., Composite medium with simultaneously negative permeability and permittivity. Physical Review Letters 2000 84 18 4184 4187 2-s2.0-0346876659
37. Zhang S., Fan W., Panoiu N. C., Malloy K. J., Osgood R. M., Brueck S. R. J., Experimental demonstration of near-infrared negative-index metamaterials. Physical Review Letters 2005 95 13 137404 10.1103/PhysRevLett.95.137404 (Pubitemid 41505612)
38. Shalaev V. M., Cai W., Chettiar U. K., Yuan H. K., Sarychev A. K., Drachev V. P., Kildishev A. V., Negative index of refraction in optical metamaterials. Optics Letters 2005 30 24 3356 3358 2-s2.0-30744476777 10.1364/OL.30.003356 (Pubitemid 43099202)
39. Dolling G., Wegener M., Soukoulis C. M., Linden S., Negative-index metamaterial at 780 nm wavelength. Optics Letters 2007 32 1 53 55 2-s2.0-33846699629 10.1364/OL.32.000053
40. Pendry J. B., Negative refraction makes a perfect lens. Physical Review Letters 2000 85 18 3966 3969 10.1103/PhysRevLett.85.3966 (Pubitemid 32027228)
41. Fang N., Lee H., Sun C., Zhang X., Sub-diffraction-limited optical imaging with a silver superlens. Science 2005 308 5721 534 537 2-s2.0-17644419669 10.1126/science.1108759 (Pubitemid 40570580)
42. Pendry J. B., Schurig D., Smith D. R., Controlling electromagnetic fields. Science 2006 312 5781 1780 1782 2-s2.0-33745487138 10.1126/science. 1125907 (Pubitemid 43962892)
43. Leonhardt U., Optical conformal mapping. Science 2006 312 5781 1777 1780 2-s2.0-33745511017 10.1126/science.1126493 (Pubitemid 43962891)
44. Schurig D., Mock J. J., Justice B. J., Cummer S. A., Pendry J. B., Starr A. F., Smith D. R., Metamaterial electromagnetic cloak at microwave frequencies. Science 2006 314 5801 977 980 2-s2.0-33750336551 10.1126/science.1133628 (Pubitemid 44749939)
45. Rahm M., Schurig D., Roberts D. A., Cummer S. A., Smith D. R., Pendry J. B., Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell's equations. Photonics and Nanostructures 2008 6 1 87 95 2-s2.0-40749139332 10.1016/j.photonics.2007.07.013 (Pubitemid 351389829)
46. Yang T., Chen H., Luo X., Ma H., Superscatterer: enhancement of scattering with complementary media. Optics Express 2008 16 22 18545 18550 2-s2.0-55349089226 10.1364/OE.16.018545
47. Chen H. Y., Chan C. T., Transformation media that rotate electromagnetic fields. Applied Physics Letters 2007 90 24 241105 10.1063/1.2748302 (Pubitemid 46934734)
48. Lai Y., Ng J., Chen H. Y., Han D., Xiao J., Zhang Z. Q., Chan C. T., Illusion optics: the optical transformation of an object into another object. Physical Review Letters 2009 102 25 253902 10.1103/PhysRevLett.102.253902
49. Silveirinha M., Engheta N., Tunneling of electromagnetic energy through subwavelength channels and bends using ε -near-zero materials. Physical Review Letters 2006 97 15 157403 10.1103/PhysRevLett.97.157403 (Pubitemid 44547767)
50. Silveirinha M., Engheta N., Design of matched zero-index metamaterials using nonmagnetic inclusions in ε -near-zero media. Physical Review B 2007 75 7 075119 10.1103/PhysRevB.75.075119
51. Silveirinha M. G., Engheta N., Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε near-zero metamaterials. Physical Review B 2007 76 24 245109 10.1103/PhysRevB.76.245109
52. Alu A., Engheta N., Dielectric sensing in ε -near-zero narrow waveguide channels. Physical Review B 2008 78 045102
53. Alu A., Silveirinha M. G., Engheta N., Transmission-line analysis of ε -near-zerofilled narrow channels. Physical Review E 2008 78 1 016604 10.1103/PhysRevE.78.016604
54. Edwards B., Alu A., Silveirinha M. G., Engheta N., Reflectionless sharp bends and corners in waveguides using ε -near-zero effects. Journal of Applied Physics 2009 105 4 044905 10.1063/1.3074506
55. Liu R., Cheng Q., Hand T., Mock J. J., Cui T. J., Cummer S. A., Smith D. R., Experimental demonstration of electromagnetic tunneling through an ε -near-zero metamaterial at microwave frequencies. Physical Review Letters 2008 100 2 023903 10.1103/PhysRevLett.100.023903
56. Edwards B., Alu A., Young M. E., Silveirinha M., Engheta N., Experimental verification of ε -near-zero metamaterial coupling and energy squeezing using a microwave waveguide. Physical Review Letters 2008 100 3 033903 10.1103/PhysRevLett.100.033903 (Pubitemid 351161827)
57. Halterman K., Feng S., Resonant transmission of electromagnetic fields through subwavelength zero- slits. Physical Review A 2008 78 2 021805 10.1103/PhysRevA.78.021805
58. Ziolkowski R. W., Propagation in and scattering from a matched metamaterial having a zero index of refraction. Physical Review E 2004 70 4 046608 10.1103/PhysRevE.70.046608 (Pubitemid 40015648)
59. Enoch S., Tayeb G., Sabouroux P., Guerin N., Vincent P., A metamaterial for directive emission. Physical Review Letters 2002 89 21 213902 10.1103/PhysRevLett.89.213902
60. Alu A., Silveirinha M. G., Salandrino A., Engheta N., ε -near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern. Physical Review B 2007 75 15 155410 10.1103/PhysRevB.75.155410
61. Hao J., Yan W., Qiu M., Super-reflection and cloaking based on zero index metamaterial. Applied Physics Letters 2010 96 10 101109 10.1063/1.3359428
62. Jin Y., He S., Enhancing and suppressing radiation with some permeability-near-zero structures. Optics Express 2010 18 16 16587 16593 2-s2.0-77955636449 10.1364/OE.18.016587
63. Nguyen V. C., Chen L., Halterman K., Total transmission and total reflection by zero index metamaterials with defects. Physical Review Letters 2010 105 23 233908 10.1103/PhysRevLett.105.233908
64. Xu Y., Chen H., Total reflection and transmission by ε -near-zero metamaterials with defects. Applied Physics Letters 2011 98 11 113501 10.1063/1.3565172
65. Wang L. G., Wang Z. G., Zhang J. X., Zhu S. Y., Realization of Dirac point with double cones in optics. Optics Letters 2009 34 10 1510 10.1364/OL.34.001510
66. Huang X., Lai Y., Hang Z. H., Zheng H., Chan C. T., Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials. Nature Materials 2011 10 8 582 586 2-s2.0-79960641117 10.1038/nmat3030
67. Berry M. V., Quantal phase factors accompanying adiabatic changes. Proceedings of the Royal Society of London A 1984 392 1802 45 57 10.1098/rspa.1984.0023
68. Wu Y., Li J., Zhang Z. Q., Chan C. T., Effective medium theory for magnetodielectric composites: beyond the long-wavelength limit. Physical Review B 2006 74 8 085111 10.1103/PhysRevB.74.085111 (Pubitemid 44246529)
69. Gabrielli L. H., Cardenas J., Poitras C. B., Lipson M., Silicon nanostructure cloak operating at optical frequencies. Nature Photonics 2009 3 8 461 463 2-s2.0-68749084502 10.1038/nphoton.2009.117
70. Sakoda K., Optical Properties of Photonic Crystals 2004 2nd Berlin, Germany Springer-Verlag
71. Chong Y. D., Wen X. G., Soljacic M., Effective theory of quadratic degeneracies. Physical Review B 2008 77 23 235125 10.1103/PhysRevB.77.235125
72. Sakoda K., Zhou H., Role of structural electromagnetic resonances in a steerable left-handed antenna. Optics Express 2010 18 26 27371 27386 2-s2.0-78650583520 10.1364/OE.18.027371
73. Sakoda K., Zhou H., Analytical study of two-dimensional degenerate metamaterial antennas. Optics Express 2011 19 15 13899 13921 2-s2.0-79960479655 10.1364/OE.19.013899
74. Sakoda K., Dirac cone in two- and three-dimensional metamaterials. Optics Express 2012 20 4 3898 3917 10.1364/OE.20.003898
75. Sakoda K., Double Dirac cones in triangular-lattice metamaterials. Optics Express 2012 20 9 9925 9939 10.1364/OE.20.009925
76. Inui T., Tanabe Y., Onodera Y., Group Theory and Its Applications in Physics 1990 Berlin, Germany Springer
77. Mei J., Wu Y., Chan C. T., Zhang Z. Q., Do linear dispersions of classical waves mean Dirac cones? Physical Review B 2012 86 035141 10.1103/PhysRevB.86.035141
78. Lan Z., Goldman N., Bermudez A., Lu W., Ohberg P., Dirac-Weyl fermions with arbitrary spin in two-dimensional optical superlattices. Physical Review B 2011 84 16 165115 10.1103/PhysRevB.84.165115
79. Dora B., Kailasvuori J., Moessner R., Lattice generalization of the Dirac equation to general spin and the role of the flat band. Physical Review B 2011 84 19 195422 10.1103/PhysRevB.84.195422
80. Akkermans E., Wolf P. E., Maynard R., Coherent backscattering of light by disordered media: analysis of the peak line shape. Physical Review Letters 1986 56 14 1471 1474 10.1103/PhysRevLett.56.1471
81. Costa J. T., Silveirinha M. G., Mimicking the Veselago-Pendry lens with broadband matched double-negative metamaterials. Physical Review B 2011 84 15 155131 10.1103/PhysRevB.84.155131
82. Chan C. T., Huang X., Liu F., Hang Z. H., Dirac dispersion and zero-index in two dimensional and three dimensional photonic and phononic systems. Progress In Electromagnetics Research B 2012 44 163 190 10.2528/PIERB12082103